1. Memory management, part 2: outline
Page replacement algorithms
Modeling PR algorithms
Working-set model and algorithms
Virtual memory implementation issues
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

2. Page Replacement Algorithms
Page fault forces choice
which page must be removed to make room for incoming page?
Modified page must first be saved
unmodified just overwritten
Better not to choose an often used page
will probably need to be brought back in soon
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

3. Optimal page replacement algorithm
Remove the page that will be referenced latest
Unrealistic: assumes we know future sequence of page references
Example 7 5 1
3 page frames
Assume that, starting from this configuration, the sequence of (virtual) page references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First page to remove is last to be used…
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

4. Optimal page replacement algorithm
Remove the page that will be referenced latest
Unrealistic: assumes we know future sequence of page references
Example 7 5
Assume that, starting from this configuration, the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First page to remove is last to be used…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

5. Optimal page replacement algorithm
Remove the page that will be referenced latest
Unrealistic: assumes we know future sequence of page references
Example 7 4
Assume that, starting from this configuration, the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First page to remove is last to be used…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

6. Optimal page replacement algorithm
Remove the page that will be referenced latest
Unrealistic: assumes we know future sequence of page references
Example 7 2
Assume that, starting from this configuration, the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First page to remove is last to be used…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

7. Optimal page replacement algorithm
Remove the page that will be referenced latest
Unrealistic: assumes we know future sequence of page references
Example 7 1
Assume that, starting from this configuration, the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
3 page frames
Altogether 4 page replacements. What if we used FIFO?
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

8. Optimal vs. FIFO Example7 5 1
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

9. Optimal vs. FIFO Example5 1
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

10. Optimal vs. FIFO Example4 1
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

11. Optimal vs. FIFO Example4 7
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

12. Optimal vs. FIFO Example2 4 7
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

13. Optimal vs. FIFO Example2 1 7
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

14. Optimal vs. FIFO Example2 1
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
First in first out…
3 page frames
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

15. Optimal vs. FIFO Example7 1
Assume that, starting from this configuration (7,5,1), the sequence of references is: 0, 5, 4, 7, 0, 2, 1, 0, 7
3 page frames
FIFO does 7 replacements, 3 more than optimal.
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

16. Page replacement: NRU - Not Recently Used
There are 4 classes of pages, according to the referenced and modified bits
Select a page at random from the least-needed class
Easy scheme to implement
Prefers a frequently referenced (unmodified) page on an “old modified” page
How can a page belong to class B?
Referenced=false
Referenced=true
Modified=false A C
Modified=true B D 16
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

17. 2'nd chance FIFO replacement algorithm
May be implemented by using a queue
FIFO: “oldest” page may be most referenced page
An improvement: “second chance” FIFO
Inspect pages from oldest to newest
If page's referenced bit is on, give it a second chance:
Clear bit
Move to end of queue
Else
Remove page
“Second chance” FIFO can be implemented more efficiently as a circular queue: the “clock algorithm”
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

18. Second Chance Page Replacement Algorithm
Operation of second chance FIFO
pages sorted in FIFO order
Page list if fault occurs at time 20, A has R bit set (numbers above pages are times of insertion to list)
When A moves forward its R bit is cleared, timestamp updated
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

19. The Clock Page Replacement Algorithm
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

20. LRU - Least Recently Used
Most recently used pages have high probability of being referenced again
Replace page used least recently
Not easy to implement – total order must be maintained
Possible hardware solutions
Use a large HW-manipulated counter, store counter value in page entry on each reference, select page with smallest value.
Use an nXn bit array (see next slide)
When page-frame k is referenced, set all bits of row k to 1 and all bits of column k to 0.
The row with lowest binary value is least recently used
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

21. LRU with bit tables Reference string is: 0,1,2,3,2,1,0,3,2,3 1 2 2 3 11 2 3 3
Reference string is: 0,1,2,3,2,1,0,3,2,3
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

22. Why is this algorithm correct?
Claim 1
The diagonal is always composed of 0’s.
Claim 2
Right after a page i is referenced, matrix row i has the maximum binary value (all other rows
have at least one more 0 in addition to that in the i’th column)
Claim 3
For all distinct i, j, k, a reference to page k does not change the order between matrix
lines i, j.
A new referenced page gets line with maximum value and does not change previous
order, so a simple induction proof works.
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

23. NFU - Not Frequently Used Approximating LRU in software
In order to record frequently used pages add a counter field to each page frame – but don’t update on each memory reference, update every clock tick.
At each clock tick, add the R bit to the counters (and zero the bit)
Select page with lowest counter for replacement
problem: remembers everything…
remedy (an “aging” algorithm):
shift-right the counter before adding the reference bit
add the reference bit at the left (Most Significant Bit)
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

24. NFU - the “aging” simulation version
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

25. Differences between LRU and NFU
If two pages have the same number of zeroes before the first ‘1’, whom should we select? (E.g., processes 3, 5 after (e) )
If two pages have 0 counters, whom should we select? (counter has too few bits…)
Therefore NFU is only an approximation of LRU.
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

26. Memory management, part 2: outline
Page replacement algorithms
Modeling PR algorithms
Working-set model and algorithms
Virtual memory implementation issues
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

27. Belady's anomaly Belady’s anomaly
The same algorithm may cause MORE page faults with MORE page frames!
Example: FIFO with reference string
Youngest frame 1 2 3 4
Oldest frame P P P P P P P P P
9 page faults
Youngest frame 1 2 3 4
Oldest frame P P P P P P P P P P
10 page faults!
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

28. Modeling page replacement algorithms
Reference string – sequence of page accesses made by process
number of virtual pages n
number of physical page frames m (we assume a single process)
a page replacement algorithm
can be represented by an array M of n rows 1 m n
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

29. Stack Algorithms Stack algorithms do not suffer from Belady’s anomaly
M(m, r): for a fixed process P, the set of virtual pages in memory after the r’th reference of process P, with memory size m.
Definition: stack algorithms
A page replacement algorithm is a stack algorithm if, for every P, m and reference string r, it holds that M(m, r)  M(m+1, r)
Stack algorithms do not suffer from Belady’s anomaly
Example: LRU, optimal replacement
FIFO is not a stack algorithm
Useful definition
Distance string: distance of referenced page from top of stack
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

30. Probability density functions for two hypothetical distance strings
The Distance String
Probability density functions for two hypothetical distance strings
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

31. Computing page faults number
Ci is the number of times that i is in the distance string
The number of page faults when we have m page frames is
Fm =
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

32. Back to page replacement algorithms Taking multiprogramming into account
Local vs. global algorithms
“Fair share” is not the best policy (static !!)
allocate according to process size – so, so…
must be a minimum for running a process...
Age A6 A6
Local policy
Global policy
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

33. Thrashing
If a process does not have “enough” pages, the page-fault rate is very high. This leads to:
Low CPU utilization
`Chain reaction’ may cause OS to think it needs to increase the degree of multiprogramming
More processes added to the system
Thrashing  a process busy in swapping pages in and out
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

34. Thrashing Diagram
CPU utilization
degree of multiprogramming
thrashing
Increasing multiprogramming level initially increases CPU utilization
Beyond some point, thrashing sets in and multiprogramming level must be decreased.
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

35. Process thrashing as function of page frames #
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

36. The impact of page-faults
for a page-fault rate p, memory access time of 100 nanosecs and page-fault service time of 25 millisecs the effective access time is (1-p) x p x 25,000,000
for p=0.001 the effective access time is still larger than 100 nanosecs by a factor of 250
for a goal of only 10% degradation in access time we need p = …
difficult to know how much frames to allocate to processes – differ in size; structure; priority;…
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

37. Memory management, part 2: outline
Page replacement algorithms
Modeling PR algorithms
Working-set model and algorithms
Virtual memory implementation issues
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

38. Working-Set Model: assumptions
Locality of reference: during any phase of execution, a process is accessing a small number of pages – the process' working set.
Process migrates from one locality to the other; localities may overlap
If assigned physical memory is smaller than working set we get thrashing
The working set of a process is the set of pages used by the Δ most recent memory references (for some predetermined Δ)
WS(t) denotes the size of the working set in time t (for some fixed Δ)
Optional: use pre-paging to bring a process' WS
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

39. Working set model  t1 t2 WS(t1) = {1,2,5,6,7} WS(t2) = {3,4}
page reference table  t1 t2
WS(t1) = {1,2,5,6,7}
WS(t2) = {3,4}
Figure Working-set model
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

40. Working-Set Model
Δ  working-set window  a fixed number of page references
If Δ too small - will not encompass entire locality.
If Δ too large - will encompass several localities.
If Δ =   will encompass entire program.
Dt =  WS(t)  total size of all working sets in time t
If Dt > m  thrashing
Policy: if D > m, then suspend one of the processes.
How can we estimate WS(t) without doing an update every memory reference?
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

41. Dynamic set + Aging
the working-set window cannot be based on memory references - too expensive
one way to enlarge the time gap between updates is to use some clock tick triggering
reference bits are updated by the hardware
Virtual time maintained for each process (in PCB entry)
every timer tick, update process virtual time and virtual time of referenced paging-table entries; then the R bit is cleared
Page p’s age is the diff between the process' virtual time and the time of p's last reference
At PF time, the table is scanned and the entry with R=0 and the largest “age” is selected for eviction
We use process virtual time (rather than global time) since it is more correlated to the process' working set
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

42. The Working Set Page Replacement Algorithm (2)
The working set algorithm
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

43. The WSClock Page Replacement Algorithm4
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

44. Dynamic set - Clock Algorithm
WSClock is in practice a global clock algorithm - for pages held by all processes in memory
Circling the clock, the algorithm uses the reference bit and an additional data structure, ref(frame), is set to the current “virtual time” of the process
WSClock: Use an additional condition that measures “elapsed (process) time” and compares it to 
replace page when two conditions apply
reference bit is unset
Tp - ref(frame) > 
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

45. Dynamic set - WSClock Example
3 processes p0, p1 and p2
current (virtual) times of the 3 processes are
Tp0 = 50; Tp1 = 70; Tp2 = 90
WSClock: replace when Tp - ref(frame) > 
the minimal distance (“window size”) is  = 20
The clock hand is currently pointing to page frame 4
page-frames:
ref. bit:
process ID:
last ref:
>20
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

46. Review of Page Replacement Algorithms
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

47. Memory management, part 2: outline
Page replacement algorithms
Modeling PR algorithms
Working-set model and algorithms
Virtual memory implementation issues
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

48. Operating system involvement in paging
Upon new process creation
Determine initial size of program + data
Create a page table: allocate space, initialize
Allocate space in swap area
Initialize swap area
Update info about page-table and swap area in PTE
Upon process scheduling for execution
Reset MMU and flush TLB
Select new process' page table as current
Optionally bring some of the processes pages to memory
Upon process exit
Release page table, pages and swap area
Don't release shared pages if still referenced
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

49. Valid (In-memory) Bit
With each page table entry a bit is associated (1  in-memory, 0  not-in-memory)
Initially, valid-invalid is set to 0 on all entries
During address translation, if in-memory bit in page table entry is 0  page fault
Valid (In-memory) bit
Frame # 1
Page table
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

50. Page Fault
If there is ever a reference to a page, first reference will trap to OS  page fault
OS looks at the valid bit to decide:
Invalid reference  abort
Just not in memory
Get empty frame (page replacement algorithm)
Swap page into frame
Update PTE, in-memory bit = 1
Restart instruction:
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

51. Handling page faults
The MMU sends a hardware interrupt, PC saved on stack
Registers are saved, kernel is called
Kernel discovers the virtual page that caused fault
Kernel checks valid bit and verifies protection. If illegal access – send signal to process. Otherwise…
Check for a free page frame. If non available, apply a page replacement algorithm
If selected page frame is dirty – write to disk (context switch). Mark frame as busy
When page frame is clean, read from disk (process still suspended)
When page arrives, update page table, mark frame as normal state
Upon process re-scheduling, re-execute faulting instruction, reload registers, continue execution
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

52. Instruction backup
MOVE.L #6(A1), 2(A0)
16 bits
1000
Move
1002 6
Block Move
1004 2
Above instruction makes 3 memory accesses. How does kernel know which caused the fault and where the instruction starts?
If instruction does auto-increment/decrement, how do we know if it was already done?
Some machines provide this info in hardware registers,
Otherwise, OS sweats…
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

53. Memory access with page faults
P = probability of a page fault
MA = memory access time
PF = time to process page faults
EMA – Effective Memory Access =
(1-p) x MA + P x PF
where
PF = page-fault interrupt service time +
Read-in page time (maybe write-page too?) +
Restart process time
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

54. Demand Paging Bring a page into memory only when it is needed
Less memory needed
Faster response
More users
Page is needed  reference it
Invalid reference  abort
not-in-memory  bring to memory
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

55. Locking Pages in Memory
Virtual memory and I/O occasionally interact
Process A issues read from I/O device into buffer
DMA transfer begins, process A blocks
process B starts executing
Process B causes a page fault
Page including buffer copied to by DMA may be chosen to be paged out
Need to be able to lock page until I/O completes
Page exempted from being considered for replacement
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

56. Page Sharing
Multiple processes may execute same code, we would like the text pages to be shared
Paging out process A pages may cause many page faults for process B that shares them
looking up for “evicted” pages in all page tables is impossible
solution: maintain special data structures for shared pages
Data pages may be shared also. E.g., when doing fork(), the copy-on-write mechanism.
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

57. Cleaning Policy Pre-paging more efficient than pure demand-paging
Often implemented by paging daemon
periodically inspects state of memory. Cleans pages, possibly removing them
When too few frames are free
selects pages to evict using a replacement algorithm
It can use same circular list (clock)
as regular page replacement algorithm but with a different pointer
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

58. Handling the backing store
need to store non-resident pages on disk swap area
Alternative 1 (static) : allocate a fixed chunk of the swap area to process upon creation, keep offset in PTE
Problem: memory requirements may change dynamically
Alternative 2: Reserve separate swap areas for text, data, stack, allow each to extend over multiple chunks
Alternative 3 (dynamic) : allocate swap space to a page when it is swapped out, de-allocate when back in.
Need to keep swap address for each page
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

59. Backing Store (a) Paging to static swap area
(b) Backing up pages dynamically
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

60. Virtual Memory - Advantages
Programs may use much smaller physical memory than their maximum requirements (much code or data is unused…)
Higher level of multiprogramming
Programs can use much larger (virtual) memory
simplifies programming and enable using powerful software
swapping time is smaller
External fragmentation is eliminated
More flexible memory protection (but less so than segmentation…)
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan

61. Virtual Memory - Disadvantages
Special hardware for address translation - some instructions may require 5-6 address translations!
Difficulties in restarting instructions (chip/microcode complexity)
Complexity of OS!
Overhead - a Page-fault is an expensive operation in terms of both CPU and I/O overhead.
Page-faults bad for real time
Thrashing problem
Ben-Gurion University Operating Systems, 2012, Danny Hendler and Roie Zivan